A182676 a(n) is the largest n-digit number with exactly 8 divisors, a(n) = 0 if no such number exists.

0, 88, 999, 9994, 99995, 999994, 9999994, 99999994, 999999998, 9999999995, 99999999998, 999999999998, 9999999999998, 99999999999998, 999999999999995, 9999999999999998, 99999999999999998, 999999999999999987, 9999999999999999995, 99999999999999999985, 999999999999999999995

Offset

1,2

Comments

a(n) is the largest n-digit number of the form p^7, p^3*q or p*q*r (p, q, r = distinct primes), a(n) = 0 if no such number exists.

Links

Amiram Eldar, Table of n, a(n) for n = 1..100

Formula

a(n) = max {10^(n-1) <= k < 10^n : A000005(k)=8} if set is nonempty, else a(n) = 0.

Maple

with(numtheory):
a:= proc(n) local k;
      if n<2 then 0
    else for k from 10^n-1 while tau(k)<>8 by -1
         do od; k
      fi
    end:
seq(a(n), n=1..20);

Prog

(PARI) a(n)=forstep(k=10^n-1, 10^(n-1), -1, numdiv(k)==8 & return(k)) \\ M. F. Hasler, Nov 27 2010

Crossrefs

Cf. A000005, A030626, A182675.

Sequence in context: A227479 A321061 A295591 * A228744 A249294 A239274

Adjacent sequences: A182673 A182674 A182675 * A182677 A182678 A182679

Keyword

nonn,base

Author

Jaroslav Krizek, Nov 27 2010

Extensions

Edited by Alois P. Heinz, Nov 27 2010

Given terms double-checked with given PARI code by M. F. Hasler, Nov 27 2010

a(20)-a(21) from Amiram Eldar, Apr 09 2024

Status

approved